Random and Vector Measures

This comprehensive text treats the complementary subjects of random and vector measures. A vector-valued measure is a function on a ring of sets taking values in a vector space, and a random measure is a subclass of vector measures whose value spaces are built on a probability space. There is a common foundation for both, yet each has different application potentials. The book examines the representations of random and vector measures, random measures on probability (i.e., Fréchet, Banach, and Hilbert) spaces, the bimeasures associated with random measures and the extension to polymeasures, boundedness principles, and the importance of random and vector measures in applications. The interaction between random and vector measures is explained, thus helping to understand the deeper aspects of vector-valued analysis. This comparative and distinctive text is ideal for either graduate students in the classroom setting, or for researchers in mathematics, statistics, and engineering.